Trap spacing measurements (In meters) of a sample of seven teams of red spiny lobster fishermen are reproduced in the accompanying table. Let H represent the average of the trap spacing measurements for the population of red spiny lobster fishermen. The mean and the standard deviation of the sample measurements are X = 88 meters and s = 12.4 meters, respectively. Suppose you want to determine if the true value differs from 95 meters. Complete the parts below:
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a. Specify the null and alternative hypotheses for this test.
Ho: H = 95
Ha: H ≠ 95
b. Since X = 88 is less than 95, the fisherman wants to reject the null hypothesis. What are the problems with using such a decision rule?
To reject the null hypothesis, the problem must specify the critical value of z. To reject the null hypothesis, the problem must specify the value of α and the probability that the test will lead to rejection, and then consult the table depending on the size of the sample. To reject the null hypothesis, the problem must specify the sample size. To reject the null hypothesis, the problem must specify the critical value of t.
c. Compute the value of the test statistic.
(Round to two decimal places as needed)
d. Find the approximate p-value of the test.
p-value
(Round to three decimal places as needed)
Select a value of α, the probability of Type I error. Interpret this value in the words of the problem:
There would still be sufficient evidence to reject the null hypothesis if α > 0.001.
Interpret this value in the words of the problem:
Type I error would be to conclude that the true mean of the trap spacing measurements is not 95 when in fact, the mean is equal to 95.
Give the appropriate conclusion based on the results of parts c and d. Let α = 0.05.
Fail to reject Ho: There is insufficient evidence to indicate H ≠ 95.